Free · Physics models
Approximate Bow Speed and Arrow Mechanics
Evaluate a disclosed empirical bow-speed adjustment and derive arrow momentum and kinetic energy.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
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Formula and method
arrow speed = 91.440; momentum = 2.0738. This worked example uses the displayed units and declared assumptions.
arrow_weight * arrow_speed^2 /2 *6.47989e-5 *0.3048^2= kin_energy; arrow_weight * arrow_speed *6.47989e-5 *0.3048 = momentum; arrow_speed= IBO + (draw_length-30)*10 -add_weight/3 +min(0, (-(arrow_weight-draw_weight* 5)/3))
Worked example
Enter these known values and leave the other values blank.
- Bow IBO rating
- 91.44 m/s
- Draw length of the bow
- 76.2 cm
- Peak draw weight
- 31.7514659 kg
- Arrow weight
- 350 gr
- Additional weight on string
- 0 gr
- Speed
- 91.44 m/s
- Momentum
- 2.074 N⋅s
- Kinetic energy
- 94.82 J
Assumptions and limitations
- Bow speed is a captured empirical estimate based on IBO rating and linear adjustments. It is not a universal bow law or measured performance: consult chronograph measurements and equipment data.
- Momentum and kinetic energy use the captured rounded grain-to-kilogram factor 6.47989e-5; speed conversion is exactly 0.3048 meters per foot. Draw weight is represented by pound-equivalent standard-gravity mass.
Common questions
What assumptions apply?
Bow speed is a captured empirical estimate based on IBO rating and linear adjustments. It is not a universal bow law or measured performance: consult chronograph measurements and equipment data.
Which unknowns can I solve?
Editable controls preserve the supported captured inverse branches. Clear the desired unknown and provide enough independent known quantities; singular or underdetermined inverses may remain incomplete.
References
Bow speed is a captured empirical estimate based on IBO rating and linear adjustments. It is not a universal bow law or measured performance: consult chronograph measurements and equipment data. Momentum and kinetic energy use the captured rounded grain-to-kilogram factor 6.47989e-5; speed conversion is exactly 0.3048 meters per foot. Draw weight is represented by pound-equivalent standard-gravity mass.